Mercurial > hg > octave-lyh
annotate libinterp/corefcn/eig.cc @ 17289:bc924baa2c4e
doc: Add new @qcode macro for code samples which are quoted.
Macro handles options ("on") or properties ("position") more elegantly
than @code{"text"}.
* doc/interpreter/macros.texi: Add new @qcode macro.
* doc/interpreter/tips.txi: Add documentation about @qcode macro.
* doc/interpreter/basics.txi, doc/interpreter/container.txi,
doc/interpreter/emacs.txi, doc/interpreter/errors.txi,
doc/interpreter/eval.txi, doc/interpreter/expr.txi,
doc/interpreter/external.txi, doc/interpreter/func.txi,
doc/interpreter/grammar.txi, doc/interpreter/image.txi,
doc/interpreter/install.txi, doc/interpreter/interp.txi,
doc/interpreter/io.txi, doc/interpreter/matrix.txi,
doc/interpreter/numbers.txi, doc/interpreter/oop.txi,
doc/interpreter/package.txi, doc/interpreter/plot.txi,
doc/interpreter/quad.txi, doc/interpreter/sparse.txi,
doc/interpreter/strings.txi, doc/interpreter/system.txi,
doc/interpreter/vectorize.txi, libinterp/corefcn/balance.cc,
libinterp/corefcn/bitfcns.cc, libinterp/corefcn/cellfun.cc,
libinterp/corefcn/conv2.cc, libinterp/corefcn/data.cc,
libinterp/corefcn/debug.cc, libinterp/corefcn/defaults.cc,
libinterp/corefcn/dirfns.cc, libinterp/corefcn/dlmread.cc,
libinterp/corefcn/error.cc, libinterp/corefcn/file-io.cc,
libinterp/corefcn/find.cc, libinterp/corefcn/gammainc.cc,
libinterp/corefcn/graphics.cc, libinterp/corefcn/help.cc,
libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc,
libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc,
libinterp/corefcn/ls-oct-ascii.cc, libinterp/corefcn/lu.cc,
libinterp/corefcn/luinc.cc, libinterp/corefcn/matrix_type.cc,
libinterp/corefcn/oct-hist.cc, libinterp/corefcn/pager.cc,
libinterp/corefcn/pr-output.cc, libinterp/corefcn/pt-jit.cc,
libinterp/corefcn/qz.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc,
libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sparse.cc,
libinterp/corefcn/spparms.cc, libinterp/corefcn/str2double.cc,
libinterp/corefcn/svd.cc, libinterp/corefcn/symtab.cc,
libinterp/corefcn/syscalls.cc, libinterp/corefcn/toplev.cc,
libinterp/corefcn/tril.cc, libinterp/corefcn/typecast.cc,
libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc,
libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/chol.cc,
libinterp/dldfcn/colamd.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc,
libinterp/dldfcn/symbfact.cc, libinterp/octave-value/ov-base.cc,
libinterp/octave-value/ov-fcn-handle.cc,
libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc,
libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-usr-fcn.cc, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/pt-binop.cc, libinterp/parse-tree/pt-eval.cc,
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scripts/java/javaclasspath.m, scripts/java/usejava.m,
scripts/miscellaneous/bzip2.m, scripts/miscellaneous/computer.m,
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scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m,
scripts/optimization/fminunc.m, scripts/optimization/fsolve.m,
scripts/optimization/fzero.m, scripts/optimization/glpk.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/optimset.m,
scripts/optimization/pqpnonneg.m, scripts/pkg/pkg.m, scripts/plot/allchild.m,
scripts/plot/ancestor.m, scripts/plot/area.m, scripts/plot/axis.m,
scripts/plot/bar.m, scripts/plot/barh.m, scripts/plot/box.m,
scripts/plot/caxis.m, scripts/plot/cla.m, scripts/plot/clabel.m,
scripts/plot/clf.m, scripts/plot/close.m, scripts/plot/colorbar.m,
scripts/plot/daspect.m, scripts/plot/ezmesh.m, scripts/plot/ezmeshc.m,
scripts/plot/ezsurf.m, scripts/plot/ezsurfc.m, scripts/plot/findall.m,
scripts/plot/findobj.m, scripts/plot/gcbo.m, scripts/plot/gcf.m,
scripts/plot/gco.m, scripts/plot/grid.m, scripts/plot/guihandles.m,
scripts/plot/hdl2struct.m, scripts/plot/hidden.m, scripts/plot/hold.m,
scripts/plot/isonormals.m, scripts/plot/isosurface.m, scripts/plot/legend.m,
scripts/plot/mesh.m, scripts/plot/meshc.m, scripts/plot/meshz.m,
scripts/plot/newplot.m, scripts/plot/orient.m, scripts/plot/pareto.m,
scripts/plot/patch.m, scripts/plot/pbaspect.m, scripts/plot/pcolor.m,
scripts/plot/plot.m, scripts/plot/print.m,
scripts/plot/private/__add_default_menu__.m, scripts/plot/quiver.m,
scripts/plot/quiver3.m, scripts/plot/refreshdata.m, scripts/plot/saveas.m,
scripts/plot/scatter.m, scripts/plot/scatter3.m, scripts/plot/shading.m,
scripts/plot/shrinkfaces.m, scripts/plot/slice.m, scripts/plot/stem.m,
scripts/plot/stem3.m, scripts/plot/struct2hdl.m, scripts/plot/subplot.m,
scripts/plot/surf.m, scripts/plot/surfc.m, scripts/plot/surfl.m,
scripts/plot/tetramesh.m, scripts/plot/uigetfile.m, scripts/plot/uimenu.m,
scripts/plot/uiputfile.m, scripts/plot/waterfall.m, scripts/plot/whitebg.m,
scripts/plot/xlim.m, scripts/plot/ylim.m, scripts/plot/zlim.m,
scripts/polynomial/conv.m, scripts/polynomial/polyout.m,
scripts/polynomial/splinefit.m, scripts/set/ismember.m, scripts/set/powerset.m,
scripts/set/setdiff.m, scripts/set/union.m, scripts/set/unique.m,
scripts/signal/detrend.m, scripts/signal/filter2.m, scripts/signal/freqz.m,
scripts/signal/periodogram.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/sparse/eigs.m, scripts/sparse/svds.m,
scripts/specfun/legendre.m, scripts/special-matrix/gallery.m,
scripts/statistics/base/mean.m, scripts/statistics/base/moment.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/sign_test.m,
scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m, scripts/strings/base2dec.m,
scripts/strings/index.m, scripts/strings/isstrprop.m,
scripts/strings/mat2str.m, scripts/strings/regexptranslate.m,
scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m,
scripts/strings/strjust.m, scripts/strings/strmatch.m,
scripts/strings/validatestring.m, scripts/testfun/demo.m,
scripts/testfun/example.m, scripts/testfun/test.m, scripts/time/addtodate.m,
scripts/time/asctime.m, scripts/time/datestr.m, scripts/time/datetick.m,
scripts/time/weekday.m, scripts/ui/errordlg.m, scripts/ui/helpdlg.m,
scripts/ui/inputdlg.m, scripts/ui/listdlg.m, scripts/ui/msgbox.m,
scripts/ui/questdlg.m, scripts/ui/warndlg.m: Use new @qcode macro.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 19 Aug 2013 20:46:38 -0700 |
parents | 2fc554ffbc28 |
children |
rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2012 John W. Eaton |
2928 | 4 |
5 This file is part of Octave. | |
6 | |
7 Octave is free software; you can redistribute it and/or modify it | |
8 under the terms of the GNU General Public License as published by the | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
2928 | 11 |
12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 for more details. | |
16 | |
17 You should have received a copy of the GNU General Public License | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
19 <http://www.gnu.org/licenses/>. | |
2928 | 20 |
21 */ | |
22 | |
23 #ifdef HAVE_CONFIG_H | |
24 #include <config.h> | |
25 #endif | |
26 | |
27 #include "EIG.h" | |
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28 #include "fEIG.h" |
2928 | 29 |
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30 #include "defun.h" |
2928 | 31 #include "error.h" |
32 #include "gripes.h" | |
33 #include "oct-obj.h" | |
34 #include "utils.h" | |
35 | |
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36 DEFUN (eig, args, nargout, |
3548 | 37 "-*- texinfo -*-\n\ |
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38 @deftypefn {Built-in Function} {@var{lambda} =} eig (@var{A})\n\ |
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39 @deftypefnx {Built-in Function} {@var{lambda} =} eig (@var{A}, @var{B})\n\ |
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40 @deftypefnx {Built-in Function} {[@var{V}, @var{lambda}] =} eig (@var{A})\n\ |
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41 @deftypefnx {Built-in Function} {[@var{V}, @var{lambda}] =} eig (@var{A}, @var{B})\n\ |
14885 | 42 Compute the eigenvalues (and optionally the eigenvectors) of a matrix\n\ |
43 or a pair of matrices\n\ | |
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44 \n\ |
14885 | 45 The algorithm used depends on whether there are one or two input\n\ |
46 matrices, if they are real or complex and if they are symmetric\n\ | |
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47 (Hermitian if complex) or non-symmetric.\n\ |
5829 | 48 \n\ |
49 The eigenvalues returned by @code{eig} are not ordered.\n\ | |
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50 @seealso{eigs, svd}\n\ |
3372 | 51 @end deftypefn") |
2928 | 52 { |
53 octave_value_list retval; | |
54 | |
55 int nargin = args.length (); | |
56 | |
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57 if (nargin > 2 || nargin == 0 || nargout > 2) |
2928 | 58 { |
5823 | 59 print_usage (); |
2928 | 60 return retval; |
61 } | |
62 | |
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63 octave_value arg_a, arg_b; |
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64 |
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65 octave_idx_type nr_a = 0, nr_b = 0; |
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66 octave_idx_type nc_a = 0, nc_b = 0; |
2928 | 67 |
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68 arg_a = args(0); |
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69 nr_a = arg_a.rows (); |
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70 nc_a = arg_a.columns (); |
2928 | 71 |
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72 int arg_is_empty = empty_arg ("eig", nr_a, nc_a); |
2928 | 73 if (arg_is_empty < 0) |
74 return retval; | |
75 else if (arg_is_empty > 0) | |
76 return octave_value_list (2, Matrix ()); | |
77 | |
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78 if (!(arg_a.is_single_type () || arg_a.is_double_type ())) |
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79 { |
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80 gripe_wrong_type_arg ("eig", arg_a); |
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81 return retval; |
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82 } |
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83 |
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84 if (nargin == 2) |
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85 { |
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86 arg_b = args(1); |
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87 nr_b = arg_b.rows (); |
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88 nc_b = arg_b.columns (); |
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89 |
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90 arg_is_empty = empty_arg ("eig", nr_b, nc_b); |
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91 if (arg_is_empty < 0) |
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92 return retval; |
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93 else if (arg_is_empty > 0) |
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94 return octave_value_list (2, Matrix ()); |
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95 |
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96 if (!(arg_b.is_single_type () || arg_b.is_double_type ())) |
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97 { |
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98 gripe_wrong_type_arg ("eig", arg_b); |
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99 return retval; |
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100 } |
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101 } |
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102 |
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103 if (nr_a != nc_a) |
2928 | 104 { |
105 gripe_square_matrix_required ("eig"); | |
106 return retval; | |
107 } | |
108 | |
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109 if (nargin == 2 && nr_b != nc_b) |
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110 { |
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111 gripe_square_matrix_required ("eig"); |
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112 return retval; |
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113 } |
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114 |
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115 Matrix tmp_a, tmp_b; |
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116 ComplexMatrix ctmp_a, ctmp_b; |
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117 FloatMatrix ftmp_a, ftmp_b; |
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118 FloatComplexMatrix fctmp_a, fctmp_b; |
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119 |
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120 if (arg_a.is_single_type ()) |
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121 { |
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122 FloatEIG result; |
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124 if (nargin == 1) |
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125 { |
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126 if (arg_a.is_real_type ()) |
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127 { |
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128 ftmp_a = arg_a.float_matrix_value (); |
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129 |
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130 if (error_state) |
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131 return retval; |
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132 else |
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133 result = FloatEIG (ftmp_a, nargout > 1); |
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134 } |
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135 else |
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136 { |
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137 fctmp_a = arg_a.float_complex_matrix_value (); |
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138 |
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139 if (error_state) |
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140 return retval; |
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141 else |
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142 result = FloatEIG (fctmp_a, nargout > 1); |
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143 } |
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144 } |
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145 else if (nargin == 2) |
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146 { |
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147 if (arg_a.is_real_type () && arg_b.is_real_type ()) |
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148 { |
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149 ftmp_a = arg_a.float_matrix_value (); |
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150 ftmp_b = arg_b.float_matrix_value (); |
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152 if (error_state) |
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153 return retval; |
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154 else |
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155 result = FloatEIG (ftmp_a, ftmp_b, nargout > 1); |
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156 } |
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157 else |
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158 { |
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159 fctmp_a = arg_a.float_complex_matrix_value (); |
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160 fctmp_b = arg_b.float_complex_matrix_value (); |
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161 |
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162 if (error_state) |
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163 return retval; |
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164 else |
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165 result = FloatEIG (fctmp_a, fctmp_b, nargout > 1); |
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166 } |
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167 } |
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169 if (! error_state) |
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170 { |
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171 if (nargout == 0 || nargout == 1) |
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172 { |
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173 retval(0) = result.eigenvalues (); |
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174 } |
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175 else |
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176 { |
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177 // Blame it on Matlab. |
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178 |
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179 FloatComplexDiagMatrix d (result.eigenvalues ()); |
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180 |
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181 retval(1) = d; |
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182 retval(0) = result.eigenvectors (); |
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183 } |
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184 } |
2928 | 185 } |
186 else | |
187 { | |
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188 EIG result; |
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189 |
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190 if (nargin == 1) |
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191 { |
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192 if (arg_a.is_real_type ()) |
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193 { |
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194 tmp_a = arg_a.matrix_value (); |
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195 |
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196 if (error_state) |
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197 return retval; |
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198 else |
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199 result = EIG (tmp_a, nargout > 1); |
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200 } |
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201 else |
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202 { |
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203 ctmp_a = arg_a.complex_matrix_value (); |
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204 |
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205 if (error_state) |
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206 return retval; |
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207 else |
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208 result = EIG (ctmp_a, nargout > 1); |
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209 } |
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210 } |
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211 else if (nargin == 2) |
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212 { |
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213 if (arg_a.is_real_type () && arg_b.is_real_type ()) |
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214 { |
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215 tmp_a = arg_a.matrix_value (); |
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216 tmp_b = arg_b.matrix_value (); |
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217 |
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218 if (error_state) |
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219 return retval; |
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220 else |
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221 result = EIG (tmp_a, tmp_b, nargout > 1); |
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222 } |
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223 else |
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224 { |
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225 ctmp_a = arg_a.complex_matrix_value (); |
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226 ctmp_b = arg_b.complex_matrix_value (); |
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227 |
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228 if (error_state) |
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229 return retval; |
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230 else |
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231 result = EIG (ctmp_a, ctmp_b, nargout > 1); |
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232 } |
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233 } |
2928 | 234 |
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235 if (! error_state) |
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236 { |
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237 if (nargout == 0 || nargout == 1) |
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238 { |
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239 retval(0) = result.eigenvalues (); |
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240 } |
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241 else |
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242 { |
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|
243 // Blame it on Matlab. |
2928 | 244 |
10154
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245 ComplexDiagMatrix d (result.eigenvalues ()); |
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246 |
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247 retval(1) = d; |
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248 retval(0) = result.eigenvectors (); |
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249 } |
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250 } |
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252 | |
253 return retval; | |
254 } | |
255 | |
256 /* | |
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257 %!assert (eig ([1, 2; 2, 1]), [-1; 3], sqrt (eps)) |
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258 |
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259 %!test |
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260 %! [v, d] = eig ([1, 2; 2, 1]); |
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261 %! x = 1 / sqrt (2); |
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262 %! assert (d, [-1, 0; 0, 3], sqrt (eps)); |
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263 %! assert (v, [-x, x; x, x], sqrt (eps)); |
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264 |
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265 %!assert (eig (single ([1, 2; 2, 1])), single ([-1; 3]), sqrt (eps ("single"))) |
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266 |
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267 %!test |
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268 %! [v, d] = eig (single ([1, 2; 2, 1])); |
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269 %! x = single (1 / sqrt (2)); |
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270 %! assert (d, single ([-1, 0; 0, 3]), sqrt (eps ("single"))); |
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271 %! assert (v, [-x, x; x, x], sqrt (eps ("single"))); |
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272 |
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273 %!test |
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274 %! A = [1, 2; -1, 1]; B = [3, 3; 1, 2]; |
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275 %! [v, d] = eig (A, B); |
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276 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); |
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277 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); |
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278 |
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279 %!test |
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280 %! A = single ([1, 2; -1, 1]); B = single ([3, 3; 1, 2]); |
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281 %! [v, d] = eig (A, B); |
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282 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single"))); |
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283 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); |
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284 |
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285 %!test |
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286 %! A = [1, 2; 2, 1]; B = [3, -2; -2, 3]; |
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287 %! [v, d] = eig (A, B); |
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288 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); |
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289 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); |
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290 |
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291 %!test |
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292 %! A = single ([1, 2; 2, 1]); B = single ([3, -2; -2, 3]); |
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293 %! [v, d] = eig (A, B); |
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294 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single"))); |
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295 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); |
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296 |
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297 %!test |
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298 %! A = [1+3i, 2+i; 2-i, 1+3i]; B = [5+9i, 2+i; 2-i, 5+9i]; |
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299 %! [v, d] = eig (A, B); |
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300 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); |
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301 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); |
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302 |
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303 %!test |
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304 %! A = single ([1+3i, 2+i; 2-i, 1+3i]); B = single ([5+9i, 2+i; 2-i, 5+9i]); |
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305 %! [v, d] = eig (A, B); |
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306 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single"))); |
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307 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); |
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308 |
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309 %!test |
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310 %! A = [1+3i, 2+3i; 3-8i, 8+3i]; B = [8+i, 3+i; 4-9i, 3+i]; |
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311 %! [v, d] = eig (A, B); |
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312 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); |
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313 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); |
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314 |
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315 %!test |
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316 %! A = single ([1+3i, 2+3i; 3-8i, 8+3i]); B = single ([8+i, 3+i; 4-9i, 3+i]); |
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317 %! [v, d] = eig (A, B); |
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318 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single"))); |
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319 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); |
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320 |
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321 %!test |
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322 %! A = [1, 2; 3, 8]; B = [8, 3; 4, 3]; |
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323 %! [v, d] = eig (A, B); |
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324 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); |
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325 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); |
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326 |
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327 %!error eig () |
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328 %!error eig ([1, 2; 3, 4], [4, 3; 2, 1], 1) |
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329 %!error <EIG requires same size matrices> eig ([1, 2; 3, 4], 2) |
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330 %!error <argument must be a square matrix> eig ([1, 2; 3, 4; 5, 6]) |
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331 %!error <wrong type argument> eig ("abcd") |
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332 %!error <wrong type argument> eig ([1 2 ; 2 3], "abcd") |
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333 %!error <wrong type argument> eig (false, [1 2 ; 2 3]) |
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